CN107506529A - A kind of Composite Material Stiffened Panel Axial Compression Stability computational methods - Google Patents
A kind of Composite Material Stiffened Panel Axial Compression Stability computational methods Download PDFInfo
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Abstract
The present invention relates to a kind of Composite Material Stiffened Panel Axial Compression Stability computational methods, the computation model of Composite Material Stiffened Panel is determined first, because the Composite Material Stiffened Panel is made up of covering and multiple ribs uniformly arranged, therefore the typical unit between two neighboring rib is analyzed, and establish coordinate system；Secondly support coefficient of the rib to covering is determined, if support coefficient of the rib to covering is kL, support coefficient of another rib to covering is kR, then k is worked asL=kRWhen=0, rib is freely-supported to the status of support of covering, works as kL=kRDuring=∞, rib be to the status of support of covering it is clamped, but rib to the status of support of covering between freely-supported and it is clamped between, therefore establish the expression formula that rib supports covering coefficient k；Finally determine Composite Material Stiffened Panel Axial Compression Stability Critical Buckling Load.During the Composite Material Stiffened Panel axle compressive load computational methods of the present invention, computational accuracy is very close with result of the test, and computational accuracy is high, it is easy to calculate.
Description
Technical field
The invention belongs to aeronautic structure intensive analysis field, more particularly to a kind of Composite Material Stiffened Panel Axial Compression Stability
Computational methods.
Background technology
Existing composite Materials Design handbook and airplane design reference do not account for rib to Stiffened
Board shaft press stability influence, do not provide yet rib to covering elasticity support (status of support between freely-supported and it is clamped between)
When, the stability formula under Material Stiffened Panel axle compressive load.By being arranged to substantial amounts of test data analyzer, using existing at present
The initial buckling load and the deviation of test value that some Engineering Algorithms obtain are bigger, and some calculation errors are even as high as 30%~
40%.To find out its cause, during application project calculation formula, the boundary condition of Axial Compression Stability considers according to simply supported on four sides, causes to count
It is too conservative to calculate result；But if pressing clamped consideration, relatively danger, is unfavorable for aircraft safety again.In fact, sinew adding strip is to covering
The support of skin between freely-supported and it is clamped between, belong to elasticity support category.In order to improve analysis precision, composite knot is improved
Structure service efficiency, there is an urgent need to be modified engineering analysis method, obtain accurately calculating composite stiffened axle pressure just
The formula of beginning buckling load.
The content of the invention
It is an object of the invention to provide a kind of Composite Material Stiffened Panel Axial Compression Stability computational methods, for solving at present
In the axle compressive load method for calculating Composite Material Stiffened Panel, influence of the rib to covering only have freely-supported and it is clamped two kinds it is extreme
The drawbacks of state so that it is larger to its result of calculation deviation the problem of.
To reach above-mentioned purpose, the technical solution adopted by the present invention is：A kind of Composite Material Stiffened Panel Axial Compression Stability
Computational methods, it is first determined the computation model of Composite Material Stiffened Panel, due to the Composite Material Stiffened Panel by covering and
Multiple rib compositions uniformly arranged, therefore the typical unit between two neighboring rib is analyzed, and establish coordinate system；Its
The secondary support coefficient for determining rib to covering, if support coefficient of the rib to covering is kL, support of another rib to covering
Coefficient is kR, then k is worked asL=kRWhen=0, rib is freely-supported to the status of support of covering, works as kL=kRDuring=∞, rib is to covering
Status of support to be clamped, but rib to the status of support of covering between freely-supported and it is clamped between, therefore establish rib and covering supported
The expression formula of coefficient k；Finally determine Composite Material Stiffened Panel Axial Compression Stability Critical Buckling Load.
Further, the Composite Material Stiffened Panel in the present invention sets its length as a, and width B, rib spacing is b, by
To the equal cloth beam compressive load N of unit lengthxEffect, therefore the establishment of coordinate system criterion is：With Composite Material Stiffened Panel
Length direction is x directions, and width is y directions, and z is to meeting right-handed coordinate system.
Further, in the present invention, the rib of foundation supports that covering the expression formula of coefficient k is specially：
In formula：Dij(i, j=1,2,6) is the bending stiffness matrix of composite material laminated board, and footmark skin refers to covering,
Stringer refers to rib.
Further, in the present invention, the process of Composite Material Stiffened Panel Axial Compression Stability Critical Buckling Load is determined
Specially：
For the typical unit of foundation, due to rib to the status of support of covering between freely-supported and it is clamped between, that is, belong to
Elasticity is supported, therefore displacement function w (x, the y) expression formula for setting z directions is：
In formula：β is constant；M is numbers of half wave of the Composite Material Stiffened Panel along x directions； To be normal
Several, it is determined by displacement boundary conditions；
Wherein displacement boundary conditions are：
Finally determine that displacement function w (x, y) expression formula is according to displacement boundary conditions：
Afterwards, the elastic strain energy of Composite Material Stiffened Panel is designated as Ue, along the elastic strain energy on plate elasticity support side
It is designated as UΓ, along the load N of loading directionxThe external work done is designated as V, then total potential energy ∏ of Composite Material Stiffened Panel is：
Π=Ue+UΓ-V；
According to minimum potential energy principal, then have：δ Π=δ Ue+δUΓ- δ V=0
Wherein：
Bring displacement function w (x, y) expression formula into minimum potential energy principal, buckling load N can be obtainedxFor：
OrderCritical Buckling Load can be obtainedExpression formula is：
In formula, each coefficient expressions are as follows：
The Composite Material Stiffened Panel Axial Compression Stability computational methods of the present invention propose one kind and are related to rib support first
The Composite Material Stiffened Panel Axial Compression Stability computational methods of effect, solve existing reference and calculating Stiffened
When board shaft presses buckling load, it is believed that the status of support of rib only has freely-supported and clamped two kinds of extremities, thus does not give
Go out when support of the rib to covering between freely-supported and it is clamped between (i.e. rib is supported covering elasticity) when buckling load calculate
The problem of formula, and the present invention is when then by the derivation of equation, rib is supported covering elasticity, composite stiffened axle pressure is steady
Qualitative calculation formula, and then the elastic support pattern and practical structures status of support that propose are closer.The composite of the present invention
Material Stiffened Panel Axial Compression Stability computational methods solve current Engineering Algorithm when calculating the Stability of Stiffened Plates of composite, institute
Computational solution precision is higher, calculating process is easy.
Brief description of the drawings
Accompanying drawing herein is merged in specification and forms the part of this specification, shows the implementation for meeting the present invention
Example, and for explaining principle of the invention together with specification.
Fig. 1 is the Composite Material Stiffened Panel structural representation in the present invention.
Fig. 2 is the typical unit structure chart in the present invention.
Fig. 3 is the composite rib sectional view of one embodiment of the invention.
Fig. 4 is the computational methods and comparison of test results figure using the present invention.
Embodiment
To make the purpose, technical scheme and advantage that the present invention is implemented clearer, below in conjunction with the embodiment of the present invention
Accompanying drawing, the technical scheme in the embodiment of the present invention is further described in more detail.
The Composite Material Stiffened Panel Axial Compression Stability computational methods of the present invention, comprise the following steps：
Step 1: determine Composite Material Stiffened Panel computation model
Composite Material Stiffened Panel as shown in Figure 1, Composite Material Stiffened Panel are made up of covering and rib, wherein, cover
Skin and rib are that composite is made.The entire length (the namely length of rib) of Composite Material Stiffened Panel is a, width
For B, rib spacing is b, by the equal cloth beam compressive load N of unit lengthxEffect, axle compressive load NxAction direction and rib
Diameter parallel.The typical unit between two consecutive webs is taken to be analyzed, as shown in Figure 2.Define composite and add wallboard
Length direction (namely rib axis direction) is x directions, and width is y directions, and z meets the right hand to (perpendicular to x/y plane)
Coordinate system.Support coefficient of the rib in left side to covering is designated as kL, support coefficient of the right side rib to covering be designated as kR。
Step 2: determine support coefficient k of the rib to covering
Work as kL=kRIt is that rib is freely-supported to the status of support of covering when=0, kL=kRDuring=∞, be rib to covering
Support to be clamped.But in fact, rib to the status of support of covering between freely-supported and it is clamped between, therefore establish rib to covering
Support coefficient k, its support coefficient k expression formula be：
In formula：Dij(i, j=1,2,6) is the bending stiffness matrix of composite material laminated board, and footmark skin refers to covering,
Stringer refers to rib.
Step 3: determine Composite Material Stiffened Panel Axial Compression Stability Critical Buckling Load
For the typical unit in Fig. 2, (support of the rib to covering is supported because support of the rib to covering belongs to elasticity
State between freely-supported and it is clamped between state be referred to as elasticity and support), displacement function w (x, the y) expression formula in setting z directions is：
In above formula, β is constant；M is numbers of half wave of the plate along x directions；, can be by position for constant term
Boundary condition is moved to determine.
Displacement boundary conditions are as follows：
Finally it can finally determine that displacement function w (x, y) expression formula is according to boundary condition：
Wherein, Dij(i, j=1,2,6) is the bending stiffness matrix of composite material laminated board.
The elastic strain energy of Composite Material Stiffened Panel is designated as Ue, support the elastic strain energy on side to be designated as along plate elasticity
UΓ, along loading direction external force NxThe external work done is designated as V, and total potential energy ∏ of plate is：
Π=Ue+UΓ-V
According to minimum potential energy principal, then have：δ Π=δ Ue+δUΓ- δ V=0
Wherein：
Afterwards, bring displacement function w (x, y) expression formula into minimum potential energy principal, buckling load N can be obtainedxFor：
OrderCritical Buckling Load can be obtainedExpression formula is：
In above formula, each coefficient expressions are as follows：
Pass through above-mentioned calculating and formula, you can try to achieve Critical Buckling Load
In order that the Composite Material Stiffened Panel Axial Compression Stability computational methods of the present invention more understand, below with a certain tool
Volume data is done to the Composite Material Stiffened Panel Axial Compression Stability computational methods of the present invention and further described in detail.
It is known：Certain technique for aircraft composite Material Stiffened Panel structure, wherein covering material therefor are CF3031/3238A fabrics, long
Purlin (being same effect with the rib in the present invention) material therefor is CF3031/3238A fabrics and CCF300/323A one-way tapes,
The ply sequence of covering is [(± 45)/(0/90)/(± 45)/(0/90)/(± 45)], and stringer ply sequence is：[(±45)/
02/(±45)/02/(±45)]s, by axle compressive load NxEffect.The length of Composite Material Stiffened Panel is a=500mm, stringer
Spacing is b=200mm, and stringer section (section) is T profile, and the height of stringer is 20mm, and section bar top surface width is 25mm, stringer
Section shape and size as shown in Figure 3, the material property of multiple material used in the present embodiment is shown in Table 1.
The material property table of table 1
| Material trademark | Longitudinal tensile MPa | Cross directional stretch modulus MPa | Longitudinal-transverse shear modulus MPa | Poisson's ratio |
| 3238A/CCF300 | 125000 | 8280 | 3700 | 0.3 |
| 3238A/CF3031 | 59200 | 58000 | 3770 | 0.054 |
Firstly the need of the model for determining to calculate, if support coefficient of the rib to covering is k, due to the rib mode one of both sides
Cause, therefore kL=KR, and a=500mm, b=200mm；
It is then determined that support coefficient k of the rib to covering
According to covering and the ply sequence and material property of stringer, stringer is obtained, the bending stiffness coefficient of covering is to see
Table 2：
The bending stiffness coefficient table of table 2
With reference to data in Fig. 1 and table 1, obtaining support coefficient k of the T-shaped stringer to covering is：
Finally determine Composite Material Stiffened Panel Axial Compression Stability critical loadBut demand obtains ginseng among each first
Number, as a result for：
Further trying to achieve Critical Buckling Load is
Existing composite Materials Design handbook and airplane design reference are calculating composite stiffened axle lateral deflection song
During load, the engineering calculation formulas only under simple boundary, built-in boundary, do not provide when support of the rib to covering between
Freely-supported and it is clamped between (i.e. rib to covering elasticity support) when buckling load calculation formula.The composite of the present invention adds
Muscle wallboard computational methods have filled up this blank, and rib is added to covering when calculating composite stiffened axle pressure buckling load
Elasticity is supported, tries to achieve composite stiffened Axial Compression Stability calculation formula, and acquired results coincide very well with test value, implement effect
Fruit refers to lower Fig. 4.It is visible in Fig. 4, when support of the rib to covering is only freely-supported, result of calculation it is less than normal (it is more conservative,
Surplus is larger), when when support of the rib to covering is only clamped, result of calculation is (more dangerous, surplus is smaller) bigger than normal, if taking
Freely-supported and it is clamped between average value, without related foundation, and calculate that deviation is also larger, but using the composite of the present invention
During Material Stiffened Panel axle compressive load computational methods, computational accuracy is very close with result of the test, and computational accuracy is high, it is easy to calculate.
Present invention firstly provides a kind of Composite Material Stiffened Panel Axial Compression Stability calculating for being related to rib buttressing effect
Method, propose solve current Engineering Algorithm when calculating the stability of stiffened panel, it is believed that the status of support of rib only has freely-supported
The drawbacks of with two kinds of clamped extremities, the elastic support pattern and practical structures status of support of proposition are closer, are succeeded in one's scheme
It is higher to calculate result precision, the Composite Material Stiffened Panel axle compressive load computational methods are one great prominent in current technology field
It is broken.
It is described above, it is only the optimal embodiment of the present invention, but protection scope of the present invention is not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the change or replacement that can readily occur in,
It should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of the claim
Enclose and be defined.
Claims (4)
- A kind of 1. Composite Material Stiffened Panel Axial Compression Stability computational methods, it is characterised in that：First determine Composite Material Stiffened Panel computation model, due to the Composite Material Stiffened Panel by covering and it is multiple The rib composition of even arrangement, therefore the typical unit between two neighboring rib is analyzed, and establish coordinate system；Secondly support coefficient of the rib to covering is determined, if support coefficient of the rib to covering is kL, another rib is to covering Support coefficient is kR, then k is worked asL=kRWhen=0, rib is freely-supported to the status of support of covering, works as kL=kRDuring=∞, rib is to covering The status of support of skin to be clamped, but rib to the status of support of covering between freely-supported and it is clamped between, therefore establish rib to covering Support the expression formula of coefficient k；Finally determine Composite Material Stiffened Panel Axial Compression Stability Critical Buckling Load.
- 2. Composite Material Stiffened Panel Axial Compression Stability computational methods according to claim 1, it is characterised in that composite adds Its length of muscle wallboard is a, and width B, rib spacing is b, by the equal cloth beam compressive load N of unit lengthxEffect, thus it is described Establishment of coordinate system criterion is：Using the length direction of Composite Material Stiffened Panel as x directions, width is y directions, and z is to meeting Right-handed coordinate system.
- 3. Composite Material Stiffened Panel Axial Compression Stability computational methods according to claim 2, it is characterised in that the rib of foundation To covering support coefficient k expression formula be specially：<mrow> <mi>k</mi> <mo>=</mo> <mfrac> <mrow> <munder> <mo>&Sigma;</mo> <mi>i</mi> </munder> <msub> <mrow> <mo>&lsqb;</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mn>11</mn> </msub> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>D</mi> <mn>66</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>D</mi> <mn>12</mn> </msub> <msub> <mi>D</mi> <mn>26</mn> </msub> <msub> <mi>D</mi> <mn>16</mn> </msub> <mo>-</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <msubsup> <mi>D</mi> <mn>16</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>D</mi> <mn>66</mn> </msub> <msubsup> <mi>D</mi> <mn>12</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>D</mi> <mn>11</mn> </msub> <msubsup> <mi>D</mi> <mn>26</mn> <mn>2</mn> </msubsup> <mo>)</mo> <mo>&CenterDot;</mo> <mn>4</mn> <mi>b</mi> </mrow> <mrow> <msub> <mi>D</mi> <mn>11</mn> </msub> <msub> <mi>D</mi> <mn>22</mn> </msub> <mo>-</mo> <msubsup> <mi>D</mi> <mn>12</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>&rsqb;</mo> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mi>s</mi> <mi>t</mi> <mi>r</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mo>&CenterDot;</mo> <msub> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <mo>)</mo> </mrow> <mrow> <mi>s</mi> <mi>k</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow>In formula：Dij(i, j=1,2,6) is the bending stiffness matrix of composite material laminated board, and footmark skin refers to covering, Stringer refers to rib.
- 4. Composite Material Stiffened Panel Axial Compression Stability computational methods according to claim 3, it is characterised in that determine composite wood Material Material Stiffened Panel Axial Compression Stability Critical Buckling Load process be specially：For the typical unit of foundation, due to rib to the status of support of covering between freely-supported and it is clamped between, that is, belong to elasticity Support, therefore displacement function w (x, the y) expression formula for setting z directions is：In formula：β is constant；M is numbers of half wave of the Composite Material Stiffened Panel along x directions； For constant term, It is determined by displacement boundary conditions；Wherein displacement boundary conditions are：<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>w</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>w</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>y</mi> <mo>=</mo> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>R</mi> </msub> <msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>y</mi> <mo>=</mo> <mi>b</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>Finally determine that displacement function w (x, y) expression formula is according to displacement boundary conditions：<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>w</mi> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>{</mo> <mfrac> <mi>y</mi> <mi>b</mi> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mi>L</mi> </msub> <mi>b</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>D</mi> <mn>22</mn> </msub> </mrow> </mfrac> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>y</mi> <mi>b</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mfrac> <mrow> <mn>12</mn> <msubsup> <mi>D</mi> <mn>22</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mrow> <mn>5</mn> <msub> <mi>k</mi> <mi>L</mi> </msub> <mo>-</mo> <mn>3</mn> <msub> <mi>k</mi> <mi>R</mi> </msub> </mrow> <mo>)</mo> </mrow> <mi>b</mi> <mo>-</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <mo>&CenterDot;</mo> <msub> <mi>k</mi> <mi>R</mi> </msub> </mrow> <mrow> <mn>6</mn> <msubsup> <mi>D</mi> <mn>22</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>bk</mi> <mi>R</mi> </msub> <msub> <mi>D</mi> <mn>22</mn> </msub> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mi>y</mi> <mi>b</mi> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn>12</mn> <msubsup> <mi>D</mi> <mn>22</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mrow> <mn>4</mn> <msub> <mi>k</mi> <mi>L</mi> </msub> <mo>-</mo> <mn>4</mn> <msub> <mi>k</mi> <mi>R</mi> </msub> </mrow> <mo>)</mo> </mrow> <mi>b</mi> <mo>-</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <mo>&CenterDot;</mo> <msub> <mi>k</mi> <mi>R</mi> </msub> </mrow> <mrow> <mn>12</mn> <msubsup> <mi>D</mi> <mn>22</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mn>2</mn> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>bk</mi> <mi>R</mi> </msub> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mi>y</mi> <mi>b</mi> </mfrac> <mo>)</mo> </mrow> <mn>4</mn> </msup> <mo>}</mo> <mo>&times;</mo> <mi>&beta;</mi> <mo>&CenterDot;</mo> <mi>sin</mi> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> <mi>x</mi> </mrow> <mi>a</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>Afterwards, the elastic strain energy of Composite Material Stiffened Panel is designated as Ue, support the elastic strain energy on side to be designated as along plate elasticity UΓ, along the load N of loading directionxThe external work done is designated as V, then total potential energy ∏ of Composite Material Stiffened Panel is：Π=Ue +UΓ-V；According to minimum potential energy principal, then have：δ Π=δ Ue+δUΓ- δ V=0Wherein：<mrow> <msub> <mi>U</mi> <mi>e</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munder> <mrow> <mo>&Integral;</mo> <mo>&Integral;</mo> </mrow> <mi>&Omega;</mi> </munder> <mo>{</mo> <msub> <mi>D</mi> <mn>11</mn> </msub> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>D</mi> <mn>12</mn> </msub> <mo>&CenterDot;</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mn>4</mn> <msub> <mi>D</mi> <mn>66</mn> </msub> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&part;</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>}</mo> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> </mrow><mrow> <msub> <mi>U</mi> <mi>&Gamma;</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munder> <mo>&Integral;</mo> <mi>&Gamma;</mi> </munder> <msub> <mi>k</mi> <mi>L</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>&Gamma;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munder> <mo>&Integral;</mo> <mi>&Gamma;</mi> </munder> <msub> <mi>k</mi> <mi>R</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>y</mi> <mo>=</mo> <mi>b</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>&Gamma;</mi> </mrow><mrow> <mi>V</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>N</mi> <mi>x</mi> </msub> <munder> <mrow> <mo>&Integral;</mo> <mo>&Integral;</mo> </mrow> <mi>&Omega;</mi> </munder> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>w</mi> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> </mrow>Bring displacement function w (x, y) expression formula into minimum potential energy principal, buckling load N can be obtainedxFor：<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>N</mi> <mi>x</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msub> <mi>D</mi> <mn>11</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mn>4</mn> </msup> <msub> <mi>b&eta;</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msub> <mi>D</mi> <mn>22</mn> </msub> <mo>&CenterDot;</mo> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>3</mn> </msup> </mfrac> <mo>&CenterDot;</mo> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>D</mi> <mn>12</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <mo>&CenterDot;</mo> <msub> <mi>&eta;</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>D</mi> <mn>66</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <msub> <mi>&eta;</mi> <mn>4</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mfrac> <msub> <mi>&eta;</mi> <mn>5</mn> </msub> </mrow> <mrow> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msub> <mi>b&eta;</mi> <mn>6</mn> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>D</mi> <mn>11</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <msub> <mi>&eta;</mi> <mn>1</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>+</mo> <msub> <mi>D</mi> <mn>22</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mi>a</mi> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>4</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>-</mo> <mn>2</mn> <msub> <mi>D</mi> <mn>12</mn> </msub> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>2</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>3</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>+</mo> <mn>4</mn> <msub> <mi>D</mi> <mn>66</mn> </msub> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>2</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>4</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>a</mi> <mrow> <mi>m</mi> <mi>&pi;</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>3</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>5</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>OrderCritical Buckling Load can be obtainedExpression formula is：<mrow> <msubsup> <mi>N</mi> <mi>x</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> </msubsup> <mo>=</mo> <mfrac> <msqrt> <mrow> <msub> <mi>D</mi> <mn>11</mn> </msub> <msub> <mi>&eta;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>b&eta;</mi> <mn>5</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </msqrt> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <msqrt> <mrow> <msub> <mi>D</mi> <mn>11</mn> </msub> <msub> <mi>&eta;</mi> <mn>1</mn> </msub> </mrow> </msqrt> </mrow> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> <msqrt> <mrow> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>b&eta;</mi> <mn>5</mn> </msub> </mrow> </msqrt> </mrow> </mfrac> <mo>-</mo> <mn>2</mn> <msub> <mi>D</mi> <mn>12</mn> </msub> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>2</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>3</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>+</mo> <mn>4</mn> <msub> <mi>D</mi> <mn>66</mn> </msub> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mn>2</mn> </msup> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>4</mn> </msub> <msub> <mi>&eta;</mi> <mn>6</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <msqrt> <mrow> <msub> <mi>D</mi> <mn>11</mn> </msub> <msub> <mi>&eta;</mi> <mn>1</mn> </msub> </mrow> </msqrt> <mo>&CenterDot;</mo> </mrow> <msqrt> <mrow> <msub> <mi>D</mi> <mn>22</mn> </msub> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>b&eta;</mi> <mn>5</mn> </msub> </mrow> </msqrt> </mfrac> <mfrac> <msub> <mi>&eta;</mi> <mn>5</mn> </msub> <mrow> <msub> <mi>b&eta;</mi> <mn>6</mn> </msub> </mrow> </mfrac> </mrow>In formula, each coefficient expressions are as follows：
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| CN108256214A (en) * | 2018-01-16 | 2018-07-06 | 滨州学院 | A kind of orthogonal stiffened panel calculating method of stiffness of aviation and device |
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| CN111143941B (en) * | 2019-12-24 | 2022-10-11 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression bearing capacity of composite material reinforced wall plate |
| CN111143941A (en) * | 2019-12-24 | 2020-05-12 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression bearing capacity of composite material reinforced wall plate |
| CN111274670A (en) * | 2019-12-31 | 2020-06-12 | 中国航空工业集团公司沈阳飞机设计研究所 | Design method for axial compression bearing capacity test of titanium alloy section combined wall plate |
| CN111274670B (en) * | 2019-12-31 | 2023-08-08 | 中国航空工业集团公司沈阳飞机设计研究所 | Shaft pressure bearing capacity test design method for titanium alloy profile combined wallboard |
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| CN111948043A (en) * | 2020-07-24 | 2020-11-17 | 中国飞机强度研究所 | Buckling prediction method for stiffened wall panel under combined load action of tension, compression and shear |
| CN112560182A (en) * | 2020-12-17 | 2021-03-26 | 中航沈飞民用飞机有限责任公司 | Civil aircraft composite material reinforced wallboard stringer rigidity determination method based on stability characteristics |
| CN112711798B (en) * | 2020-12-29 | 2022-10-11 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression stability of four-side clamped composite material laminated board |
| CN112711798A (en) * | 2020-12-29 | 2021-04-27 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating axial compression stability of four-side clamped composite material laminated board |
| CN115031590A (en) * | 2022-05-19 | 2022-09-09 | 上海交通大学 | Method for optimizing structural stability of reinforced wall plate bearing joint load |
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